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Search: id:A158490
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| 90, 390, 890, 1590, 2490, 3590, 4890, 6390, 8090, 9990, 12090, 14390, 16890, 19590, 22490, 25590, 28890, 32390, 36090, 39990, 44090, 48390, 52890, 57590, 62490, 67590, 72890, 78390, 84090, 89990, 96090, 102390, 108890, 115590, 122490, 129590
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OFFSET
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1,1
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COMMENT
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If A=[A158490] 100*n.^2-10 (n>0, 90, 390, 890,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158491] 20*n^2-1 (n>0, 19, 79, 179, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 19^2-90*2^2=1; 79^2-390*4^2=1; 179^2-890*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=100*n^2-10 (n>0)
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EXAMPLE
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For N=1, a(1)=90; n=2, a(2)=390; n=3, a(3)=890
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CROSSREFS
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Cf. A005843, A158491
Sequence in context: A074213 A027621 A157888 this_sequence A066116 A156738 A065949
Adjacent sequences: A158487 A158488 A158489 this_sequence A158491 A158492 A158493
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009
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